Passive channel calibration method based on non-linear antenna array

ABSTRACT

Taught herein is a passive channel calibration method wherein a non-linear antenna array sets an antenna array to a non-linear formation that contains at least a combination of translation invariant dual array-element couples, detects single-azimuth ocean echoes via combinations of translation invariant dual array-element couples, estimates channel amplitude mismatch coefficients via the single-azimuth ocean echoes to implement amplitude calibration, and estimates channel phase mismatch coefficients via the single-azimuth ocean echoes after amplitude calibration and the known array position information to implement phase calibration.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Patent ApplicationNo. PCT/CN2006/000453 with an international filing date of Mar. 21,2006, designating the United States, now pending, and further claimspriority benefits to Chinese Patent Application No. 200510018438.3 filedMar. 24, 2005, the contents of which are incorporated herein byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a passive channel calibration method for a highfrequency surface wave radar (HFSWR) by a non-linear antenna array.

2. Description of the Related Art

High frequency surface wave radar uses the characteristic ofvertically-polarized high frequency electromagnetic wave whoseattenuation is low when it transmits along the ocean surface. It has thecapability of over-the-horizon detection of the targets below the lineof sight, such as vessels, low-altitude planes, missiles and so on. Inaddition, HFSWR can extract the ocean state information (wind field,wave field, current field, etc.) from the first order and the secondorder radar ocean echoes. Then the real time monitoring of large-scope,high-precision and all-weather to the ocean can be achieved.

Influenced by multiple factors, such as difference in hardware,non-ideal characteristic of receiving channels and surroundingelectromagnetic environment, amplitude-phase characteristics of each ofthe radar channels including antenna are different, which causesinconsistency between the amplitude and phase values of the same echosignal passing through different channels, which is referred to aschannel mismatch. The channel mismatch may increase errors of, or eveninvalidate beam scan and direction-of-arrival estimation. The channelmismatch is a key point that affects detecting performance of HFSWR.Steps must be taken to restrict the channel mismatch within a givenrange to ensure operating efficiently of the radar: firstly, propermeasurements should be taken (e.g. component selection) to ensureconsistency of each channel during production thereof; secondly, thechannel mismatch coefficients can be measured or estimated, andcharacteristic difference between channels is further reduced viacalibration.

Existing channel calibration methods can be categorized into active onesand passive ones. In the active calibration method, the auxiliary signalsource is located in an open area far away from the antenna array tosend calibration signals, and the output of each receiving channel ismeasured; then, channel mismatch information can be obtained bydeducting the phase difference caused by azimuth of known signal sourceand array space position. In the passive calibration method, noauxiliary signal source whose azimuth has been accurately obtained isneeded, the channel mismatch coefficients are estimated directly via thereceived measuring data and some apriority information (e.g. arrayformat), and compensative calibration is implemented. There are otherpassive calibration methods that can realize joint estimation of signalazimuth and channel mismatch. Detailed description of the passivecalibration method can be found in the book “Spatial Spectrum Estimationand its Applications” (Press of China University of Science andTechnology, 1997) by Liu D S and Luo J Q.

Influenced by many factors, such as landform condition, operatingwavelength, electromagnetic wave propagation, radar system, antennaarray, (solid) target echoes, ocean echoes, noise interference, it isdifficult to implement channel calibration for HFSWRs. The prior art canonly partly solve the problems, and is time-consuming and expensive. Seasurface is in front of the radar antenna array, so if the activecalibration is adopted, the auxiliary signal source can only be locatedon a ship or an island, which will be troublesome and expensive tomaintain and difficult to work steadily. Existing passive calibrationmethods need complicated iterative computing, which means a heavycomputing load and may not meet a real-time requirement, and even have apossibility of converging to the local optimum, not the global one,which may result in completely inaccurate estimated values. Applicableconditions of the existing passive calibration method cannot besatisfied due to the difference between an actual radar system and anideal model. The channel calibration has become a big technical problemthat restricts detecting performance of HFSWR and affects actualapplication thereof, and must be solved properly.

The Radio Wave Propagation Lab of Wuhan University has considered usingthe reflection signal of a known natural or artificial object on theocean as a calibration signal. The calibration signal can be detectedfrom echoes if the range and the velocity of a reflection source arealready known, and mismatch coefficients of each channel are estimatedbased on the azimuth of the reflection source. Detailed description canbe found in Chinese Patent Application No. 03128238.5 entitled “A methodfor array channel calibration using ocean echoes”. The invention mayutilize echoes from fixed reflection objects such as islands,lighthouses, drilling platforms and so on, which overcome problems suchas displacement and maintenance of auxiliary signal sources and extrahardware cost, and online real time automatic calibration may beimplemented. However, the invention is not suitable to a sea areawithout fixed reflection objects, and is affected by disadvantageousfactors such as noise interference, ship echoes, multi-path effect andso on. As that invention proposes a technology for separating anddetecting the ocean echoes with single azimuths, whose frequencyspectrums are non-overlapped, which meets basic requirements of thepassive channel calibration method of this invention, and will bedescribed in further detail below.

HFSWR commonly adopts a frequency modulated interrupted continuous wave(FMICW) waveform, which has been explained in detail in the paper“Target Detection and Tracking With a High Frequency Surface wave Radar”(Rafaat Khan, et al., IEEE Journal of Oceanic Engineering, 1994, 19(4):540-548). By the waveform, a range-Doppler (velocity) two-dimension echospectrum can be obtained by mixing, low-pass filtering, A/D convertingand two dimension FFT (shown as FIG. 1) after the ocean echoes(including those from ocean surface waves and from solid targets) entera receiver (as shown in FIG. 2). In the two-dimension echo spectrum, theocean echoes are separated according to the range and the velocity, anddistributed on many spectrum points. If coherence accumulation time ofthe second FFT (Doppler transformation) is rather long (about 10minutes), the radar may obtain very high velocity resolution, whichmeans the number of the spectrum points in the two-dimension echospectrum corresponding to the ocean echoes may be above 1000, and it issuitable to detect the single-azimuth echoes whose frequency spectrumsare non-overlapped via a statistical method.

Detection of the single-azimuth echoes is implemented by statisticalanalysis of a two-dimension echo spectrum of an array in a given form(as shown in FIG. 3). The array in a particular form is composed ofarray elements 1-4, whose position coordinates thereof is (x_(i),y_(i)), and the output of a corresponding two-dimension echo spectrumpoint is Y_(i), i=1, 2, 3, 4. An array-element couple A₁ is composed ofelements 1 and 2, and the other array-element couple A₂ is composed ofelements 3 and 4. There is translation invariance between A₁ and A₂,then $\left\{ \begin{matrix}{\left( {x_{2},y_{2}} \right) = \left( {{x_{1} + d},y_{1}} \right)} \\{\left( {x_{4},y_{4}} \right) = \left( {{x_{3} + d},y_{3}} \right)}\end{matrix}\quad \right.$

${{Defining}\quad\eta_{1}} = {\frac{Y_{2}Y_{3}}{Y_{1}Y_{4}}.}$It is easy to prove that, in an ideal condition without noise, η₁corresponding to a single-azimuth spectrum point in the two-dimensionecho spectrum is an invariable parameter, which only relates to channelmismatch and is marked as η′₁. In an actual system, the noise isinevitable, so η₁ corresponding to the single-azimuth spectrum pointsare centrally distributed around η₁. On the other hand, it can be knownfrom simple analysis and numerical modeling that η₁ corresponding to amulti-azimuth spectrum point is a variable relating to target parametersof ranges, (radial) velocities, azimuths and echo signal amplitudes,whose randomicity result in a randomly distributed state of η₁. Tosummarize, if η₁ corresponding to spectrum points that exceed asignal-noise-ratio threshold in the two-dimension echo spectrum aremarked on the complex plane, it will be found that highly-aggregativephenomena appears in only one region (around η′₁), where most of η₁ arecorresponding to the single-azimuth spectrum points.${{{Defining}\quad\eta_{2}} = \frac{Y_{2}Y_{1}^{*}}{Y_{4}Y_{3}^{*}}},$from analysis similar to the above, an aggregative region, where most ofη₂ are corresponding to the single-azimuth spectrum points, may alsoappear on the complex plane.${{{Defining}{\quad\quad}\eta_{3}} = \frac{Y_{2}Y_{4}^{*}}{Y_{1}Y_{3}^{*}}},$an aggregative region, where most of η₃ are corresponding to thesingle-azimuth spectrum points, may appear on the complex plane in thesame way.

Discovered through theoretic analysis and numerical modeling, theprobability that η₁, η₂ and η₃ corresponding to a multi-azimuth spectrumpoint simultaneously drop into their respective aggregative regions isvery small, and therefore whether η₁, η₂ and η₃ simultaneously drop intotheir respective aggregative regions can be used as a criterion todetect single-azimuth spectrum points. As a combination of translationinvariant dual array-element couples, A₁ and A₂ compose an array in agiven form for detecting single-azimuth echoes (spectrum points). Ifthere is more than one combination of translation invariant dualarray-element couples in the array, the single-azimuth spectrum pointscan be filtered out by a criterion whether a spectrum point is detectedby multiple combinations of translation invariant dual array-elementcouples. An array containing at least a combination of translationinvariant dual array-element couples, such as a uniform linear array (ora uniform plane array), is very common.

SUMMARY OF THE INVENTION

To overcome deficiencies of the prior art, an object of the invention isto provide a passive channel calibration method based on a non-linearantenna array using single-azimuth ocean echoes received by HFSWR, toreduce channel amplitude-phase mismatch and improve system performance.The non-linear antenna array is an array whose elements do not lie onthe same straight line.

To achieve the above object, in accordance with one embodiment of theinvention, provided is a passive channel calibration method based on anon-linear antenna array, comprising setting an antenna array to anon-linear formation that contains at least a combination of translationinvariant dual array-element couples; detecting single-azimuth oceanechoes via combinations of translation invariant dual array-elementcouples; estimating channel amplitude mismatch coefficients via thesingle-azimuth ocean echoes to implement amplitude calibration; andestimating channel phase mismatch coefficients via the single-azimuthocean echoes after amplitude calibration and the known array positioninformation to implement phase calibration.

In the above method, the channel amplitude mismatch coefficients areestimated by the single-azimuth ocean echoes using a equation${{\hat{g}}_{i} = \sqrt{\sum\limits_{l = 1}^{L}\quad{{{Y_{i}(l)}}^{2}/{\sum\limits_{l = 1}^{L}\quad{{Y_{1}(l)}}^{2}}}}},$where ĝ_(i) being an estimated value of the channel amplitude mismatchcoefficient of array element i, i=1, 2, . . . , M; M being the number ofarray elements; Y_(i)(l) being the output of the lth single-azimuth echoreceived by array element i, l=1, 2, . . . , L; and L being the numberof single-azimuth echoes.

In another embodiment, the channel amplitude mismatch coefficients areestimated by the single-azimuth ocean echoes using a equation${{\hat{g}}_{i} = \sqrt{\frac{1}{L}\quad{\sum\limits_{l = 1}^{L}\quad\frac{{{Y_{i}(l)}}^{2}}{{{Y_{1}(l)}}^{2}}}}},$where ĝhd i being an estimated value of the channel amplitude mismatchcoefficient of array element i, i=1, 2, . . . , M; M being the number ofarray elements; Y_(i)(l) being the output of the lth single-azimuth echoreceived by array element i, l=1, 2, . . . , L; and L being the numberof single-azimuth echoes.

In another embodiment, the channel amplitude mismatch coefficients areestimated by the single-azimuth ocean echoes using a equation${{\hat{g}}_{i} = {\sum\limits_{l = 1}^{L}\quad{{{Y_{i}(l)}}/{\sum\limits_{l = 1}^{L}\quad{{Y_{1}(l)}}}}}},$where ĝ_(i) being an estimated value of the channel amplitude mismatchcoefficient of array element i, i=1, 2, . . . , M; M being the number ofarray elements; Y_(i)(l) being the output of the lth single-azimuth echoreceived by array element i, l=1, 2, . . . , L; and L being the numberof single-azimuth echoes.

In another embodiment, the channel amplitude mismatch coefficients areestimated by the single-azimuth ocean echoes using a equation${{\hat{g}}_{i} = {\frac{1}{L}\quad{\sum\limits_{l = 1}^{L}\quad\frac{{Y_{i}(l)}}{{Y_{1}(l)}}}}},$where ĝ_(i) being an estimated value of the channel amplitude mismatchcoefficient of array element i, i=1, 2, . . . , M; M being the number ofarray elements; Y_(i)(l) being the output of the lth single-azimuth echoreceived by array element i, l=1, 2, . . . , L; and L being the numberof single-azimuth echoes.

In the invention, the channel phase mismatch coefficients are estimatedby the single-azimuth ocean echoes after amplitude calibration and theknown array position information from${\hat{\Psi} = {\arg\quad{\min\limits_{\Psi}{{Y - {f^{\prime}(\Psi)}}}^{2}}}},$where $\begin{matrix}{\Psi = \left\lbrack {\theta_{1},\theta_{2},\ldots\quad,\theta_{L},\phi_{2},\phi_{3},\ldots\quad,\phi_{M}} \right\rbrack^{T}} \\{Y = \begin{bmatrix}Y_{2} \\Y_{3} \\\vdots \\Y_{M}\end{bmatrix}} \\{Y_{i} = \left\lbrack {{Y_{i}(1)},{Y_{i}(2)},\ldots\quad,{Y_{i}(L)}} \right\rbrack^{T}} \\{{f^{\prime}(\Psi)} = \begin{bmatrix}{f_{2}^{\prime}(\Psi)} \\{f_{3}^{\prime}(\Psi)} \\\vdots \\{f_{M}^{\prime}(\Psi)}\end{bmatrix}} \\{{f_{i}^{\prime}(\Psi)} = \begin{bmatrix}{{{Y_{1}(1)}{\mathbb{e}}^{j{\lbrack{{\frac{2\quad\pi}{\lambda}{({{x_{i}\sin\quad\theta_{1}} + {y_{i}\cos\quad\theta_{1}}})}} + \phi_{i}}\rbrack}}},} \\{{{Y_{1}(2)}{\mathbb{e}}^{j{\lbrack{{\frac{2\quad\pi}{\lambda}{({{x_{i}\sin\quad\theta_{2}} + {y_{i}\cos\quad\theta_{2}}})}} + \phi_{i}}\rbrack}}},\ldots\quad,} \\{{Y_{1}(L)}{\mathbb{e}}^{j{\lbrack{{\frac{2\quad\pi}{\lambda}{({{x_{i}\sin\quad\theta_{L}} + {y_{i}\cos\quad\theta_{L}}})}} + \phi_{i}}\rbrack}}}\end{bmatrix}^{T}}\end{matrix}$θ_(l) being the arrival angle of the lth single-azimuth echo; Φ_(i)being the channel phase mismatch coefficient of array element i; (x_(i),y_(i)) being the array element position coordinates, and array element 1is the origin of coordinates, i.e. (x₁, Y₁)=(0,0); λ being the echosignal wavelength; {circumflex over (Ψ)} being the estimated value of Ψ.

In another embodiment, the channel phase mismatch coefficients areestimated via the single-azimuth ocean echoes after amplitudecalibration and the known array position information from${\hat{\Psi} = {\arg\quad{\min\limits_{\Psi}{{Y - {\overset{\sim}{f}(\Psi)}}}^{2}}}},$where $\begin{matrix}{\Psi = \left\lbrack {\theta_{1},\theta_{2},\ldots\quad,\theta_{L},\phi_{2},\phi_{3},\ldots\quad,\phi_{M}} \right\rbrack^{T}} \\{Y = \begin{bmatrix}Y_{2} \\Y_{3} \\\vdots \\Y_{M}\end{bmatrix}} \\{Y_{i} = \left\lbrack {{Y_{i}(1)},{Y_{i}(2)},\ldots\quad,{Y_{i}(L)}} \right\rbrack^{T}} \\{{\overset{\sim}{f}(\Psi)} = \begin{bmatrix}{\overset{\sim}{f_{2}}(\Psi)} \\{\overset{\sim}{f_{3}}(\Psi)} \\\vdots \\{\overset{\sim}{f_{M}}(\Psi)}\end{bmatrix}} \\{{\overset{\sim}{f_{i}}(\Psi)} = \begin{bmatrix}{{{\hat{A}(1)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{1}} + {y_{i}\cos\quad\theta_{1}}})}} + \phi_{i}}\rbrack}}},} \\{{{\hat{A}(2)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{2}} + {y_{i}\cos\quad\theta_{2}}})}} + \phi_{i}}\rbrack}}},\ldots\quad,} \\{{\hat{A}(L)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{L}} + {y_{i}\cos\quad\theta_{L}}})}} + \phi_{i}}\rbrack}}}\end{bmatrix}^{T}} \\{{\hat{A}(l)} = {\frac{1}{M}{\sum\limits_{i = 1}^{M}\quad{{Y_{i}(l)}{\mathbb{e}}^{- {j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{l}} + {y_{i}\cos\quad\theta_{l}}})}} + \phi_{i}}\rbrack}}}}}}} \\{= {\frac{1}{M}\left\{ {{\sum\limits_{i = 2}^{M}\quad{{Y_{i}(l)}{\mathbb{e}}^{- {j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{l}} + {y_{i}\cos\quad\theta_{l}}})}} + \phi_{i}}\rbrack}}}}} + {Y_{1}(l)}} \right\}}}\end{matrix}$θ_(l) being the arrival angle of the lth single-azimuth echo; Φ_(i)being the channel phase mismatch coefficient of array element i; (x_(i),y_(i)) being the array element position coordinates, and array element 1is the origin of coordinates, i.e. (x₁, y₁)=(0,0); λ being the echosignal wavelength; {circumflex over (Ψ)} being the estimated value of Ψ.

In accordance with the invention, three array elements are selected fromall array elements to form a triangular array, which is utilized by theprocesses to decrease the dimension number of global optimization, andthe channel phase mismatch coefficients are estimated via pre-estimationof initial values and local optimization methods, so as to reduce thecomputing load of multi-parameter estimation.

1) Selecting three array elements to form a triangular array, along withthree single-azimuth echoes for parameter estimation; 2) choosing anyelement of the triangular array as a reference channel and estimatingthe phase mismatch coefficients of other two channels and the arrivalangles of three single-azimuth echoes via global optimization methods;3) adding a single-azimuth echo for parameter estimation of thetriangular array, and thus obtaining its arrival angle; 4) obtainingarrival angles of other single-azimuth echoes according to step 3); 5)combining the triangular array with another array element to form a4-element array, and using all single-azimuth echoes for parameterestimation of the 4-element array, so as to obtain the channel phasemismatch coefficient of the newly-added array element; and 6) obtainingchannel phase mismatch coefficients of other array elements according tostep 5).

According to the invention, after step 4), using all single-azimuthechoes for parameter estimation of the triangular array, and regardingthe obtained estimated values of the arrival angles of single-azimuthechoes and the channel phase mismatch coefficients as initial values,more accurate estimated values of these parameters are obtained vialocal optimization methods, then the following step 5) and 6) areperformed.

After step 6), using all single-azimuth echoes for parameter estimationof the whole array, and regarding the obtained estimated values of thearrival angles of single-azimuth echoes and the channel phase mismatchcoefficients as initial values, more accurate estimated values of theseparameters are obtained via local optimization methods.

For an M-element L-form array, the array elements 1, 2, M are used forparameter estimation as a triangular array selected in step 1), so as toimplement channel phase calibration.

For a 4-element T-form array, array element 1, 2, 4 or array element 2,3, 4 are used for parameter estimation as a triangular array selected instep 1), so as to implement channel phase calibration.

For a 4-element rectangular array, any three array elements are used forparameter estimation as a triangular array selected in step 1), so as toimplement channel phase calibration.

The invention has the advantage of excellent practicability: it has nouse for any auxiliary signal source and so is a genuine passive channelcalibration method. The invention only utilizes the single-azimuthechoes, therefore the troublesome problems encountered by active channelcalibration methods, such as ship echo interference, multi-path effectand so on do not exist; utilizing a great number (may more than 100) ofhigh strength single-azimuth ocean echoes, and so having a highinformation utilization ratio that leads to good precision andsteadiness; employing special processes to reduce computing load,therefore can meet the real-time requirement; being able to operatestably without stopping for a long time as the ocean echoes always existlargely; greatly improving the application flexibility of HFSWRs, hencewhose antenna systems can be replaced, increased/decreased or movedfreely, which is hard to achieve in the past; improving detectionperformance, as well as greatly reducing development and maintenancecosts.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional diagram of a high frequency surface wave radar;

FIG. 2 is a range-Doppler (velocity) two-dimension echo spectrum diagramof a high frequency surface wave radar;

FIG. 3 is a schematic diagram illustrating an array in a given form fordetecting single-azimuth echoes;

FIG. 4 is a schematic diagram illustrating a M-element random non-lineararray of the invention;

FIG. 5 is a schematic diagram of a triangular array;

FIG. 6 is a schematic diagram of a M-element L-form array;

FIG. 7 is a schematic diagram of a 4-element rectangle array; and

FIG. 8 is a schematic diagram of a 4-element T-form array.

DETAILED DESCRIPTION OF THE INVENTION

A key point of the invention is to build a single-azimuth echo signalmodel received by a non-linear antenna array, to transfer a channelcalibration problem to a parameter estimation problem, and to obtaincomparatively accurate channel mismatch estimation.

First of all, a M-element (M≧3) random non-linear antenna array is shownin FIG. 4, and detailed embodiments in that scenario are describe below:

(A) Signal Model

The array element position coordinates of the non-linear antenna arrayshown in FIG. 4 are (x_(i), y_(i)) (i=1, 2, . . . , M), and arrayelement 1 is the origin of coordinates, i.e. (x₁, y₁i)=(0,0). An oceanecho can be regard as a plane wave. Assuming the number of thesingle-azimuth echoes detected from the range-Doppler (velocity)two-dimension echo spectrum is L (L≧3), then the output of the lth (l=1,2, . . . , L ) single-azimuth echo received by array element i is$\begin{matrix}{{Y_{i}(l)} = {g_{i}{{\mathbb{e}}^{{j\phi}_{i}}\left\lbrack {{{A(l)}{\mathbb{e}}^{j\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{l}} + {y_{i}\cos\quad\theta_{l}}})}}} + {W_{i}(l)}} \right\rbrack}}} & (1)\end{matrix}$where θ_(l) and A(l) are the arrival angle and the complex amplitude ofthe lth single-azimuth echo respectively; g_(i) and Φ_(i) are thechannel amplitude mismatch coefficient and the channel phase mismatchcoefficient of array element i respectively; λ is the echo signalwavelength; and W_(i)(l) is additive noise. Choose array element 1 as areference channel, i.e., g₁e^(jΦ) ¹ =1, it can be deduced from equation(1) thatY ₁(l)=A(l)+W ₁(l)   (2)

For the additive noise W_(i)(l), it is assumed that:

-   -   1) W_(i)(l) corresponding to different i or l are independent        from each other;    -   2) W_(i)(l) are Gauss white noise with the same variance σ².        Then the equation (1) and (2) form a signal model of channel        mismatch estimation.

(B) Channel Amplitude Calibration

The channel amplitude mismatch estimation of array element i can beobtained by $\begin{matrix}{{\hat{g}}_{i} = \sqrt{\sum\limits_{l = 1}^{L}\quad{{{Y_{i}(l)}}^{2}/{\sum\limits_{l = 1}^{L}\quad{{Y_{1}(l)}}^{2}}}}} & (3)\end{matrix}$and then the channel amplitude mismatches can be calibrated by ĝ_(i).The equation (3) has other forms such as${{\hat{g}}_{i} = \sqrt{\frac{1}{L}{\sum\limits_{l = 1}^{L}\quad\frac{{{Y_{i}(l)}}^{2}}{{{Y_{1}(l)}}^{2}}}}},{{\hat{g}}_{i} = {\sum\limits_{l = 1}^{L}\quad{{{Y_{i}(l)}}/{\sum\limits_{l = 1}^{L}\quad{{Y_{1}(l)}}}}}},{{\hat{g}}_{i} = {\frac{1}{L}{\sum\limits_{l = 1}^{L}\quad\frac{{Y_{i}(l)}}{{Y_{1}(l)}}}}},$and so on.

(C) Channel Phase Calibration

After channel amplitude calibration, the output of the lthsingle-azimuth echo received by array element i is $\begin{matrix}{{Y_{i}(l)} = {{\mathbb{e}}^{j\quad\phi_{i}}\left\lbrack {{{A(l)}{\mathbb{e}}^{j\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{l}} + {y_{i}\cos\quad\theta_{l}}})}}} + {W_{i}(l)}} \right\rbrack}} & (4)\end{matrix}$DefiningY_(i) = [Y_(i)(1), Y_(i)(2), …  , Y_(i)(L)]^(T)  i = 2, 3, …  , M$Y = \begin{bmatrix}Y_{2} \\Y_{3} \\\vdots \\Y_{M}\end{bmatrix}$ Ψ = [θ₁, θ₂, …  , θ_(L), ϕ₂, ϕ₃, …  , ϕ_(M)]^(T)${f_{i}(\Psi)} = \begin{bmatrix}{{{A(1)}{\mathbb{e}}^{j{\lbrack{{\frac{2\quad\pi}{\lambda}{({{x_{i}\sin\quad\theta_{1}} + {y_{i}\cos\quad\theta_{1}}})}} + \phi_{i}}\rbrack}}},} \\{{{A(2)}{\mathbb{e}}^{j{\lbrack{{\frac{2\quad\pi}{\lambda}{({{x_{i}\sin\quad\theta_{2}} + {y_{i}\cos\quad\theta_{2}}})}} + \phi_{i}}\rbrack}}},\ldots\quad,} \\{{A(L)}{\mathbb{e}}^{j{\lbrack{{\frac{2\quad\pi}{\lambda}{({{x_{i}\sin\quad\theta_{L}} + {y_{i}\cos\quad\theta_{L}}})}} + \phi_{i}}\rbrack}}}\end{bmatrix}^{T}$ ${f\quad(\Psi)} = \begin{bmatrix}{f_{2}(\Psi)} \\{f_{3}(\Psi)} \\\vdots \\{f_{M}(\Psi)}\end{bmatrix}$Choosing Ψ as a parameter vector to be estimated and using a maximumlikelihood method (referring to the book “Modern Signal Processing” byZhang X D, Press of Tsinghua University, 1994), according to equation(4) and noise model assumption, an estimated value of Ψ is$\begin{matrix}{\hat{\Psi} = {{\arg\quad{\min\limits_{\Psi}\left\{ {\left\lbrack {Y - {f(\Psi)}} \right\rbrack^{H}\left\lbrack {Y - {f(\Psi)}} \right\rbrack} \right\}}} = {\arg\min\limits_{\Psi}{{Y - {f(\Psi)}}}^{2}}}} & (5)\end{matrix}$where $\arg\quad\min\limits_{\Psi}$denotes a value of Ψ as an expression thereafter is minimized, ∥X∥²denotes a 2-norm of a vector X. It is apparent that the channel phasemismatch coefficients and the arrival angles of single-azimuth echoesimplement joint estimation.

A(l) cannot be obtained directly since it is contained in Y_(i)(l)having noise, and f_(i)(Ψ) cannot be constructed directly, thereforeequation (5) cannot actually be used for estimating channel phasemismatchs, and should be improved. In a condition with a common signalto noise ratio (≧20 dB), it can be inferred from equation (2) thatY₁(l)≈A(l); then replacing A(l) in equation (5) with Y₁(l), and anactual expression of the estimated value of Ψ is $\begin{matrix}{\quad{{\hat{\Psi}\quad = \quad{\arg\quad{\min\limits_{\quad\Psi}\quad{{{Y\quad - \quad{f^{\quad\prime}(\Psi)}}}^{2\quad}{where}}}}}\text{}\quad{{f^{\quad\prime}(\Psi)}\quad = \begin{bmatrix}{\quad{f_{\quad 2}^{\quad\prime}(\Psi)}} \\{\quad{f_{\quad 3}^{\quad\prime}(\Psi)}} \\\vdots \\{\quad{f_{\quad M}^{\quad\prime}(\Psi)}}\end{bmatrix}}\quad{{f_{\quad i}^{\quad\prime}(\Psi)}\quad = \quad\begin{bmatrix}{\quad{{Y_{\quad 1}(1)\quad{\mathbb{e}}^{\quad{j\lbrack\quad{{\frac{2\quad\pi}{\quad\lambda}\quad{(\quad{{x_{\quad i}\quad\sin\quad\theta_{\quad 1}}\quad + \quad{y_{\quad i}\quad\cos\quad\theta_{\quad 1}}})}}\quad + \quad\phi_{\quad i}}\rbrack}}},}\quad} \\{\quad{{Y_{\quad 1}(2)\quad{\mathbb{e}}^{\quad{j\lbrack\quad{{\frac{2\quad\pi}{\quad\lambda}\quad{(\quad{{x_{\quad i}\quad\sin\quad\theta_{\quad 2}}\quad + \quad{y_{\quad i}\quad\cos\quad\theta_{\quad 2}}})}}\quad + \quad\phi_{\quad i}}\rbrack}}},\quad\ldots\quad,}\quad} \\{\quad{Y_{\quad 1}(L)\quad{\mathbb{e}}^{\quad{j\lbrack\quad{{\frac{2\quad\pi}{\quad\lambda}\quad{(\quad{{x_{\quad i}\quad\sin\quad\theta_{\quad L}}\quad + \quad{y_{\quad i}\quad\cos\quad\theta_{\quad L}}})}}\quad + \quad\phi_{\quad i}}\rbrack}}}}\end{bmatrix}^{T}}}} & (6)\end{matrix}$and then the channel phase mismatches can be calibrated by {circumflexover (Ψ)}. If A(l) in equation (5) is replaced by other values, theequation (6) will have other forms, e.g.,${\hat{\Psi} = {\arg\quad{\min\limits_{\Psi}{{Y - {\overset{\sim}{f}(\Psi)}}}^{2}}}},$where Y and Ψ have the same definition as above, and {tilde over (f)}(Ψ)is defined as ${\overset{\sim}{f}(\Psi)} = \begin{bmatrix}{{\overset{\sim}{f}}_{2}(\Psi)} \\{{\overset{\sim}{f}}_{3}(\Psi)} \\\vdots \\{{\overset{\sim}{f}}_{M}(\Psi)}\end{bmatrix}$ $\begin{matrix}{{{\overset{\sim}{f}}_{i}(\Psi)} = \left\lbrack {{{\hat{A}(1)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{1}} + {y_{i}\cos\quad\theta_{1}}})}} + \phi_{i}}\rbrack}}},} \right.} \\{{{\hat{A}(2)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{2}} + {y_{i}\cos\quad\theta_{2}}})}} + \phi_{i}}\rbrack}}},\ldots\quad,} \\\left. {{\hat{A}(L)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{L}} + {y_{i}\cos\quad\theta_{L}}})}} + \phi_{i}}\rbrack}}} \right\rbrack^{T}\end{matrix}$ $\begin{matrix}{{\hat{A}(l)} = {\frac{1}{M}{\sum\limits_{i = 1}^{M}\quad{{Y_{i}(l)}{\mathbb{e}}^{- {j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{l}} + {y_{i}\cos\quad\theta_{l}}})}} + \phi_{i}}\rbrack}}}}}}} \\{= {\frac{1}{M}\left\{ {{\sum\limits_{i = 2}^{M}\quad{{Y_{i}(l)}{\mathbb{e}}^{- {j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{l}} + {y_{i}\cos\quad\theta_{l}}})}} + \phi_{i}}\rbrack}}}}} + {Y_{1}(l)}} \right\}}}\end{matrix}$

Theoretic analyses and simulation experiments indicate that theabove-mentioned channel phase calibration method is only applicable tonon-linear arrays and at least two single-azimuth echoes, which haveangle differences other than 0° or 180°, must be available. The channelphase mismatch estimation is actually a multidimensional parameterestimation problem and may be obtained via multidimensional searchingsince it relates to all array elements and therefore the selection ofoptimization methods. Due to the existence of local minimum, globaloptimization methods (Referring to the paper “From Local Minimum toGlobal optimization” by Tang F and Wang L, Computer Engineering andApplications, 2002.6: 56-58) must be used to estimate the channel phasemismatches. However, the methods cannot meet a real-time requirement fora very heavy computing load as there are too many parameters (more than100). The invention employs special processing to reduce the computingload, which is explained in detail below.

FIG. 5 illustrates a simplest non-linear array, which is a triangulararray constituted by three array elements not lying on the same straightline. If the channel phase mismatch coefficients of the triangular arrayand the arrival angles of single-azimuth echoes are estimated by threesingle-azimuth echoes only, a 5-dimension searching can be judged fromequation (6) (a certain array element as the reference channel). Sincefew dimensions are involved, even the global optimization methods suchas simulated annealing, evolution computing, chaos searching and randomsampling are used, the computing load of the 5-dimension searching isnot heavy, and therefore the real-time requirement can be met.

For the M-element random non-linear array as shown in FIG. 4, a certaintriangular array included therein can be used to implementpre-estimation of initial values of the parameters to be estimated, andthen local optimization methods (e.g., steepest descent method) can beused to obtain more precise estimates, so as to reduce the computingload of multi-dimension parameter estimation. Detailed steps are:

-   -   1) Choosing three array elements to form a triangular array, and        three single-azimuth echoes for parameter estimation from a        large number of ones;    -   2) Using a certain array element of the triangular array as the        reference channel, and estimating the phase mismatch        coefficients of other two channels and the arrival angles of the        three single-azimuth echoes via global optimization methods,        which is 5-dimension searching;    -   3) Adding a single-azimuth echo for parameter estimation of the        triangular array, therefore, parameters to be estimated in        equation (6) are increased by one (i.e. the arrival angle of the        newly-added single-azimuth echo), and the 5-dimension searching        is changed into 6-dimension searching; estimated values of five        parameters obtained in step 2) are substituted into equation (6)        including six parameters to be estimated, then the arrival angle        of the newly-added single-azimuth echo is estimated via        equation (6) which now has only one parameter to be estimated,        which is one-dimension searching;    -   4) Except for the three single-azimuth echoes chosen in step 1),        the arrival angle estimation of other L−3 single-azimuth echoes        can be obtained by the method in step 3).    -   5) Using all L single-azimuth echoes for parameter estimation of        the triangular array, choosing the obtained estimated values of        L+2 parameters (arrival angles of L single-azimuth echoes and        two channel phase mismatch coefficients) as initial values, and        local optimization methods are used to get more precious        estimated values of these parameters.    -   6) Combining the triangular array with another array element to        form a 4-element array and using all L single-azimuth echoes for        parameter estimation of the 4-element array, then the number of        parameters to be estimated in equation (6) is L+3; the obtained        estimated values of L+2 parameters in step 5) are substituted        into equation (6), then there is only one parameter to be        estimated in equation (6), i.e. the channel phase mismatch        coefficient of the newly-added array element, whose estimated        value can be obtained via one-dimension searching.    -   7) Except for the triangular array chosen in step 1), the        estimated values of the channel phase mismatch coefficients of        other M−3 array elements can be obtained by the method in step        6).    -   8) Using all L single-azimuth echoes for parameter estimation of        the whole M-element array, choosing the obtained estimated        values of L+M−1 parameters (arrival angles of L single-azimuth        echoes and M−1 channel phase mismatch coefficients) as initial        values, and local optimization methods are used to get more        precious estimated values of these parameters.

If the pre-estimation errors of initial values of these parameters arenot large, the result of local optimization is also the global optimum,while the computing load of local optimization is much smaller than thatof global optimization. In fact, the above pre-estimation of initialvalues takes up most of the calculating time, but it relates to theglobal optimization of 5-dimension searching at most, and therefore canmeet the real-time requirement. These eight steps above are the typicalways of special processing, and can be simplified, enriched, adjusted,or improved for practical application according to the actual situation.The basic idea is to decrease the dimension number of globaloptimization by the processing for triangular arrays, and to make themost of local optimization methods via the pre-estimation of initialvalues, so as to decrease the computing load of multi-dimensionalparameter estimation.

FIG. 6 is an M-element L-form array of an embodiment of the invention.Array element 1−M−1 form a uniform linear array, from which more thanone combination of translation invariant dual array-element couples fordetecting single-azimuth echoes can be divided. Channel amplitudecalibration can be realized by equation (3), and channel phasecalibration is the key point. A triangular array constituted by thearray element 1, 2 and M is used for estimating initial values ofparameters, and the channel phase calibration can be implemented byequation (6) and the special processing.

FIG. 7 is a 4-element rectangular array. In this embodiment, 4 arrayelements constitute only one combination of translation invariant dualarray-element couples for detecting single-azimuth echoes, and atriangular array constituted by any three array elements can be used forestimating initial values of parameters.

FIG. 8 is a 4-element T-form array. In this embodiment, the arrayelement 1-3 constitute a 3-element uniform linear array, from which onlyone combination of translation invariant dual array-element couples fordetecting single-azimuth echoes can be divided. Both the two triangulararrays constituted by the array element 1, 2, 4 and array element 2, 3,4 can be used for estimating initial values of parameters.

The channel calibration method described in the invention has gainedsuccess in high frequency surface wave radars, however, in essence, themethod is possible to be applied to other detection systems orcommunication systems receiving a large number of single-azimuthsignals.

While particular embodiments of the invention have been shown anddescribed, it will be obvious to those skilled in the art that changesand modifications may be made without departing from the invention inits broader aspects, and therefore, the aim in the appended claims is tocover all such changes and modifications as fall within the true spiritand scope of the invention.

All publications and patent applications mentioned in this specificationare indicative of the level of skill of those skilled in the art towhich this invention pertains. All publications and patent applicationsmentioned in this specification are herein incorporated by reference tothe same extent as if each individual publication or patent applicationmentioned in this specification was specifically and individuallyindicated to be incorporated by reference.

1. A passive channel calibration method based on a non-linear antennaarray, comprising: setting an antenna array to a non-linear formationthat contains at least a combination of translation invariant dualarray-element couples; detecting single-azimuth ocean echoes via saidcombinations of translation invariant dual array-element couples;estimating channel amplitude mismatch coefficients via saidsingle-azimuth ocean echoes to implement amplitude calibration; andestimating channel phase mismatch coefficients via said single-azimuthocean echoes after said amplitude calibration and the known arrayposition information to implement phase calibration.
 2. The method ofclaim 1, wherein said channel amplitude mismatch coefficients areestimated by said single-azimuth ocean echoes using the equation${\hat{g}}_{i} = \sqrt{\sum\limits_{l = 1}^{L}\quad{{{Y_{i}(l)}}^{2}/{\sum\limits_{l = 1}^{L}\quad{{Y_{1}(l)}}^{2}}}}$to implement said amplitude calibration, ĝ_(i) is an estimated value ofthe channel amplitude mismatch coefficient of array element i; i=1, 2, .. . , M; M is a number of array elements; Y_(i)(l) is an output of thelth single-azimuth echo received by said array element i; l=1, 2, . . ., L, and L is a number of said single-azimuth echoes.
 3. The method ofclaim 1, wherein said channel amplitude mismatch coefficients areestimated by said single-azimuth ocean echoes using a equation${\hat{g}}_{i} = \sqrt{\frac{1}{L}{\sum\limits_{l = 1}^{L}\quad\frac{{{Y_{i}(l)}}^{2}}{{{Y_{1}(l)}}^{2}}}}$to implement amplitude calibration; ĝ_(i) is an estimated value of thechannel amplitude mismatch coefficient of array element i; i=1, 2, . . ., M; M is a number of array elements; Y_(i)(l) being the output of thelth single-azimuth echo received by said array element i, l=1, 2, . . ., L, and L is a number of said single-azimuth echoes.
 4. The method ofclaim 1, wherein said channel amplitude mismatch coefficients areestimated by said single-azimuth ocean echoes using a equation${\hat{g}}_{i}{\underset{l = 1}{\overset{L}{= \sum}}\quad{{{Y_{i}(l)}}/{\sum\limits_{l = 1}^{L}\quad{{Y_{1}(l)}}}}}$to implement amplitude calibration; ĝ_(i) is an estimated value of thechannel amplitude mismatch coefficient of array element i; i=1, 2, . . ., M; M is a number of array elements; Y_(i)(l) is the output of the lthsingle-azimuth echo received by said array element i, l=1, 2, . . . , L,and L is a number of said single-azimuth echoes.
 5. The method of claim1, wherein said channel amplitude mismatch coefficients are estimated bysaid single-azimuth ocean echoes using a equation${\hat{g}}_{i}\underset{l = 1}{\overset{L}{= \sum}}\quad{{{Y_{i}(l)}}/{\sum\limits_{l = 1}^{L}\quad{{Y_{1}(l)}}}}$to implement amplitude calibration; ĝ_(i) is an estimated value of thechannel amplitude mismatch coefficient of array element i, i=1, 2, . . ., M; M is a number of array elements; Y_(i)(l) is the output of the lthsingle-azimuth echo received by said array element i, l=1, 2, . . . , L,and L is a number of said single-azimuth echoes.
 6. The method of claim5, wherein said channel phase mismatch coefficients are estimated bysaid single-azimuth ocean echoes after said amplitude calibration andthe known array position information from$\hat{\Psi} = {\arg\quad{\min\limits_{\Psi}{{Y - {f^{\prime}(\Psi)}}}^{2}}}$to implement phase calibration;Ψ = [θ₁, θ₂, ⋯  , θ_(L), ϕ₂, ϕ₃, ⋯  , ϕ_(M)]^(T); ${Y = \begin{bmatrix}Y_{2} \\Y_{3} \\\vdots \\Y_{M}\end{bmatrix}};$ Y_(i) = [Y_(i  )(1), Y_(i)(2), ⋯  , Y_(i)(L)]^(T);${{f^{\prime}(\Psi)} = \begin{bmatrix}{f_{2}^{\prime}(\Psi)} \\{f_{3}^{\prime}(\Psi)} \\\vdots \\{f_{M}^{\prime}(\Psi)}\end{bmatrix}};$ $\begin{matrix}{{f_{i}^{\prime}(\Psi)} = \left\lbrack {{{Y_{1}(1)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{1}} + {y_{i}\cos\quad\theta_{1}}})}} + \phi_{i}}\rbrack}}},} \right.} \\{{{Y_{1}(2)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{2}} + {y_{i}\cos\quad\theta_{2}}})}} + \phi_{i}}\rbrack}}},\cdots\quad,} \\\left. {{Y_{1}(L)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{L}} + {y_{i}\cos\quad\theta_{L}}})}} + \phi_{i}}\rbrack}}} \right\rbrack^{T}\end{matrix}$ θ_(l) is the arrival angle of the lth single-azimuth echo;Φ_(i) is the channel phase mismatch coefficient of array element i;(x_(i), y_(i)) is the array element position coordinates, and arrayelement 1 is the origin of coordinates, i.e., (x₁, y₁)=(0,0); λ is theecho signal wavelength; and {circumflex over (Ψ)} is the estimated valueof Ψ.
 7. The method of claim 6, wherein three array elements areselected from all array elements to form a triangular array; saidtriangular array is utilized by the processes to decrease the dimensionnumber of global optimization; and said channel phase mismatchcoefficients are estimated via pre-estimation of initial values andlocal optimization methods.
 8. The method of claim 5, wherein saidchannel phase mismatch coefficients are estimated by said single-azimuthocean echoes after said amplitude calibration and the known arrayposition information from$\hat{\Psi} = {\arg\quad{\min\limits_{\Psi}{{Y - {\overset{\sim}{f}(\Psi)}}}^{2}}}$to implement phase calibration;Ψ = [θ₁, θ₂, ⋯  , θ_(L), ϕ₂, ϕ₃, ⋯  , ϕ_(M)]^(T); ${Y = \begin{bmatrix}Y_{2} \\Y_{3} \\\vdots \\Y_{M}\end{bmatrix}};$ Y_(i) = [Y_(i  )(1), Y_(i)(2), ⋯  , Y_(i)(L)]^(T);${{\overset{\sim}{f}(\Psi)} = \begin{bmatrix}{{\overset{\sim}{f}}_{2}(\Psi)} \\{{\overset{\sim}{f}}_{3}(\Psi)} \\\vdots \\{{\overset{\sim}{f}}_{M}(\Psi)}\end{bmatrix}};$ $\begin{matrix}{{{\overset{\sim}{f}}_{i}(\Psi)} = \left\lbrack {{{\hat{A}(1)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{1}} + {y_{i}\cos\quad\theta_{1}}})}} + \phi_{i}}\rbrack}}},} \right.} \\{{{\hat{A}(2)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{2}} + {y_{i}\cos\quad\theta_{2}}})}} + \phi_{i}}\rbrack}}},\ldots\quad,} \\{\left. {{\hat{A}(L)}{\mathbb{e}}^{j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{L}} + {y_{i}\cos\quad\theta_{L}}})}} + \phi_{i}}\rbrack}}} \right\rbrack^{T};}\end{matrix}$ $\begin{matrix}{{\hat{A}(l)} = {\frac{1}{M}{\sum\limits_{i = 1}^{M}\quad{{Y_{i}(l)}{\mathbb{e}}^{- {j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{l}} + {y_{i}\cos\quad\theta_{l}}})}} + \phi_{i}}\rbrack}}}}}}} \\{{= {\frac{1}{M}\left\{ {{\sum\limits_{i = 2}^{M}\quad{{Y_{i}(l)}{\mathbb{e}}^{- {j{\lbrack{{\frac{2\pi}{\lambda}{({{x_{i}\sin\quad\theta_{l}} + {y_{i}\cos\quad\theta_{l}}})}} + \phi_{i}}\rbrack}}}}} + {Y_{1}(l)}} \right\}}};}\end{matrix}$ θ_(l) is the arrival angle of the lth single-azimuth echo;Φ_(i) is the channel phase mismatch coefficient of array element i;(x_(i), y_(i)) is the array element position coordinates, and arrayelement 1 is the origin of coordinates, i.e., (x₁, y₁)=(0,0); λ is theecho signal wavelength; and {circumflex over (Ψ)} is the estimated valueof Ψ.
 9. The method of claim 8, wherein three array elements areselected from all array elements to form a triangular array; saidtriangular array is utilized by the processes to decrease the dimensionnumber of global optimization; and said channel phase mismatchcoefficients are estimated via pre-estimation of initial values andlocal optimization methods
 10. The method of claim 9, comprising 1)selecting three array elements to form a triangular array, along withthree single-azimuth echoes for parameter estimation; 2) choosing anyelement of said triangular array as a reference channel and estimatingthe phase mismatch coefficients of other two channels and the arrivalangles of three single-azimuth echoes via global optimization methods;3) adding a single-azimuth echo for parameter estimation of saidtriangular array, and thus obtaining its arrival angle; 4) obtainingarrival angles of other single-azimuth echoes according to step 3); 5)combining said triangular array with another array element to form a4-element array, and using all single-azimuth echoes for parameterestimation of said 4-element array, so as to obtain the channel phasemismatch coefficient of the newly-added array element; and 6) obtainingchannel phase mismatch coefficients of other array elements according tostep 5).
 11. The method of claim 10, wherein after step 4) and beforestep 5), using all said single-azimuth echoes for parameter estimationof said triangular array, and regarding the obtained estimated values ofsaid arrival angles of said single-azimuth echoes and said channel phasemismatch coefficients as initial values, obtaining more accuratelyestimated values of these parameters via said local optimizationmethods.
 12. The method of claim 10, wherein after step 6), using allsaid single-azimuth echoes for parameter estimation of the whole array,and regarding the obtained estimated values of said arrival angles ofsaid single-azimuth echoes and said channel phase mismatch coefficientsas initial values, obtaining more accurately estimated values of theseparameters via said local optimization methods.
 13. The method of claim10, wherein for an M-element L-form array, array element 1, 2 and M areused for parameter estimation as a triangular array selected in step 1),so as to implement channel phase calibration.
 14. The method of claim10, wherein for a 4-element L-form array, array element 1, 2, 4 or arrayelement 2, 3, 4 are used for parameter estimation as a triangular arrayselected in step 1), so as to implement channel phase calibration. 15.The method of claim 10, wherein for a 4-element rectangular array, anythree array elements are used for parameter estimation as a triangulararray selected in step 1), so as to implement channel phase calibration.